class 12

Math

Algebra

Probability I

The probability that a shooter hits a target is

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Four candidates A, B, C and D have applied for the post in government office. If A is twice as likely to be selected as B, and B and C are given about the same chances of being selected, while C is twice as likely to be selected as D, what are the probabilities that (i) C will be selected? (ii) A will not be selected?

Three integers are chosen at random from the set of first 20 natural numbers. The chance that their product is a multiple of 3 is

For three events A, B and C, P(Exactly one of A or B occurs) = P (Exactly one of B or C occurs) = P (Exactly one of C or A occurs) = $41 $ and P(All the three events occurs simultaneously)= $61 $. Then the probability that at least one of the events occurs, is

The probabilities of three events A, B, and C are P(A) = 0.6, P(B) = 0.4, and P(C ) = 0.5. If $P(A∪B)$ = 0.8, $P(A∩C)=0.3$, $P(A∩B∩C)=0.2$, and $P(A∪B∪C)≥0.85$, then find the range of $P(B∩C)$.

If A and B are events such that $P(A∪B)=(3)/(4),P(A∩B)=(1)/(4)$ and $P(A_{c})=(2)/(3)$, then find (a) P(A) (b) P(B) (c ) $P(A∩B_{c})(d)P(A_{c}∩B)$

A 2n digit number starts with 2 and all its digits are prime, then the probability that the sum of any two consective digits of the number is prime is

Two friends A and B have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of A and B. The probability that all the tickets go to the daughters of A is 1/20. Find the number of daughters each of them have.

The sum of two positive quantities is equal to 2n. Find the probability that their product is not less than $3/4$ times their greatest product.